Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Average Error: 1.9 → 0.2

Time: 21.3s

Precision: 64

Math

\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]

↓

\[\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r402441 = x;
        double r402442 = y;
        double r402443 = z;
        double r402444 = r402442 - r402443;
        double r402445 = t;
        double r402446 = r402445 - r402443;
        double r402447 = 1.0;
        double r402448 = r402446 + r402447;
        double r402449 = a;
        double r402450 = r402448 / r402449;
        double r402451 = r402444 / r402450;
        double r402452 = r402441 - r402451;
        return r402452;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r402453 = a;
        double r402454 = z;
        double r402455 = y;
        double r402456 = r402454 - r402455;
        double r402457 = t;
        double r402458 = r402457 - r402454;
        double r402459 = 1.0;
        double r402460 = r402458 + r402459;
        double r402461 = r402456 / r402460;
        double r402462 = x;
        double r402463 = fma(r402453, r402461, r402462);
        return r402463;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.9
Target	0.2
Herbie	0.2

\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

1. Initial program 1.9

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))